Musings On Solvability and Unsolvable Games and Problems

It seems at any given time in our history there have been different games that were solved or unsolved. Possibly by different segments of our society perhaps rich or poor, educated or not, 1st world or 3rd world etc.  It could also be that some games are complex in such a way that certain mathematical or even technological breakthroughs must be made in order for humans to finally come up with a corresponding solution.

It is interesting to think of games we effectively cannot solve and the possibility of games that don’t have solutions.

Depending on this then some populations are effectively and literally unable to solve certain games. Unsolvability from a theoretical or intuitive stand point though is quite limited compared to effective solutions or brute force solutions that markets could produce.

Ideal money is a proposal for one such solution that realizes on Hayek’s market pricing mechanism. Ideal Poker uses this market mechanism to create an effective rake standard, essentially based on a brute force computation of poker’s GTO strategy.

Nash explains that cooperative games (or strategies) can often be solved by breaking a game down into a non-cooperative subset. There is also a suggestion in “Ideal Money” that the addition of money as a transferable utility can have a trans-formative effect on the expected payoffs: Zero sum games can become non-zero sum games.

There seems to be a difficult problem in our society, that arises all of the time and everywhere I look.  I tend to think of it in terms of the number 5.  In a simple analogue, there are 5 variables and we must balance and solve them in relation to each other. We can imagine, together, we have mastered 1, 2, 3 or 4 variable problems, but 5 is too complex.  It doesn’t really matter how we describe the game or the problem, the point is that the problem or “game” is unsolvable by theory alone since it is too complex.

But the solution is quite describable this way.  The five variables are too much to iterate and to solve in relation to each other.  So the solution here lies in separating the variables into 5 separate thinking entities with their own want to align for maximum gain. Each variable becomes a sub problem or a sub game and the solution finds itself through the interaction of these “living” parts.

The brain and mental illness or brain injury might be an example here of a problem that involves to many complex variables that must be stimulated with complex synchronicity in order for an individual to favorably heal.  Extending this, it might be that a certain strong drug addiction is such a problem that requires a specific solution unattainable by human conception alone, or at least with any current sciences we could hope to be used.

Treatment for such problems then, although helpful to some statistical degree, is necessarily determined by some chance, in relation to what ever distance we are from the solution to the complex problem.

It might not be immediately obvious to the (especially new) reader, but such a solution should prove to be quite an effective tool in the future of problems, AI, game theory etc.

Poker is also one such complex problem that we actually seem to be on the cusp of solving with this paradigm.

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s